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Grant support

SC is supported by Conicyt through its programme Becas Chile and the Cambridge overseas Trust. SC and ACD acknowledges partial support from STFC under grants ST/L000385/1 and ST/L000636/1. This work is supported in part by the EU Horizon 2020 research and innovation programme under the Marie-Sklodowska grant No. 690575. This article is based upon work related to the COST Action CA15117 (CANTATA) supported by COST (European Cooperation in Science and Technology).

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Cespedes, SebastianAuthor

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Signatures of graviton masses on the CMB

Publicated to:JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS. (3): - 2018-03-01 (3), DOI: 10.1088/1475-7516/2018/03/008

Authors: Brax, Philippe; Cespedes, Sebastian; Davis, Anne-Christine;

Affiliations

Univ Cambridge, DAMTP, Wilberforce Rd, Cambridge CB3 0WA, England - Author
Univ Paris Saclay, Inst Phys Theor, CNRS, CEA, F-91191 Gif Sur Yvette, France - Author

Abstract

The impact of the existence of gravitons with non-vanishing masses on the B-modes of the Cosmic Microwave Background (CMB) is investigated. We also focus on putative modifications to the speed of the gravitational waves. We find that a change of the graviton speed shifts the acoustic peaks of the CMB and then could be easily constrained. For the case of massive gravity, we show analytically how the B-modes are sourced in a manner differing from the massless case leading to a plateau at low l in the CMB spectrum. We also study the case when there are more than one graviton, and when pressure instabilities are present. The latter would occur in doubly coupled bigravity in the radiation era. We focus on the case where a massless graviton becomes tachyonic in the radiation era whilst a massive one remains stable. As the unstable mode decouples from matter in the radiation era, we find that the effects of the instability is largely reduced on the spectrum of B-modes as long as the unstable graviton does not grow into the non-linear regime. In all cases when both massless and massive gravitons are present, we find that the B-mode CMB spectrum is characterised by a low l plateau together with a shifted position for the first few peaks compared to a purely massive graviton spectrum, a shift which depends on the mixing between the gravitons in their coupling to matter and could serve as a hint in favour of the existence of multiple gravitons.

Keywords

Cmbr polarisationGravitational waves and cmbr polarizationModified gravityWaves

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2018, it was in position 13/69, thus managing to position itself as a Q1 (Primer Cuartil), in the category Astronomy & Astrophysics.

From a relative perspective, and based on the normalized impact indicator calculated from the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 3.53, which indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-17, the following number of citations:

  • WoS: 5
  • Scopus: 7
  • OpenCitations: 7

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-17:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 13.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 13 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 3.
  • The number of mentions on the social network Facebook: 2 (Altmetric).
  • The number of mentions on the social network X (formerly Twitter): 7 (Altmetric).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: France; United Kingdom.